Summary

Testing the effect of deviance on similarity-based structure and certainty.

Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms.

Method changes: 6 agents, 12 issues

Demographics (Attention Check)
0
(N=62)
0.25
(N=50)
0.5
(N=55)
0.75
(N=49)
1
(N=57)
Overall
(N=273)
age
Mean (SD) 37.4 (12.2) 37.8 (14.6) 34.2 (10.3) 37.2 (12.5) 37.8 (11.5) 36.9 (12.2)
Median [Min, Max] 36.5 [20.0, 64.0] 34.0 [19.0, 75.0] 34.0 [19.0, 69.0] 34.0 [18.0, 65.0] 35.0 [20.0, 64.0] 35.0 [18.0, 75.0]
race
Asian 6 (9.7%) 1 (2.0%) 6 (10.9%) 7 (14.3%) 5 (8.8%) 25 (9.2%)
Black or African-American 5 (8.1%) 2 (4.0%) 6 (10.9%) 3 (6.1%) 8 (14.0%) 24 (8.8%)
Hispanic/Latinx 10 (16.1%) 2 (4.0%) 4 (7.3%) 3 (6.1%) 4 (7.0%) 23 (8.4%)
White 41 (66.1%) 44 (88.0%) 39 (70.9%) 35 (71.4%) 39 (68.4%) 198 (72.5%)
Native Hawaiian or Other Pacific Islander 0 (0%) 1 (2.0%) 0 (0%) 0 (0%) 0 (0%) 1 (0.4%)
American Indian or Alaska Native 0 (0%) 0 (0%) 0 (0%) 1 (2.0%) 0 (0%) 1 (0.4%)
Other 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (1.8%) 1 (0.4%)
gender
Man 23 (37.1%) 23 (46.0%) 32 (58.2%) 25 (51.0%) 27 (47.4%) 130 (47.6%)
Non-binary 1 (1.6%) 1 (2.0%) 1 (1.8%) 0 (0%) 2 (3.5%) 5 (1.8%)
Woman 38 (61.3%) 26 (52.0%) 21 (38.2%) 24 (49.0%) 25 (43.9%) 134 (49.1%)
Prefer not to answer 0 (0%) 0 (0%) 1 (1.8%) 0 (0%) 2 (3.5%) 3 (1.1%)
Another gender not listed here 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (1.8%) 1 (0.4%)
0
(N=3)
0.25
(N=7)
0.5
(N=5)
0.75
(N=7)
1
(N=4)
Overall
(N=26)
age
Mean (SD) 29.7 (12.4) 39.6 (9.07) 26.4 (5.68) 38.1 (20.2) 24.3 (4.92) 33.2 (13.4)
Median [Min, Max] 23.0 [22.0, 44.0] 38.0 [30.0, 57.0] 24.0 [22.0, 36.0] 27.0 [19.0, 68.0] 24.0 [20.0, 29.0] 28.5 [19.0, 68.0]
race
White 3 (100%) 4 (57.1%) 3 (60.0%) 4 (57.1%) 2 (50.0%) 16 (61.5%)
Asian 0 (0%) 1 (14.3%) 0 (0%) 0 (0%) 0 (0%) 1 (3.8%)
Black or African-American 0 (0%) 2 (28.6%) 1 (20.0%) 3 (42.9%) 1 (25.0%) 7 (26.9%)
Hispanic/Latinx 0 (0%) 0 (0%) 1 (20.0%) 0 (0%) 1 (25.0%) 2 (7.7%)
gender
Man 1 (33.3%) 5 (71.4%) 2 (40.0%) 5 (71.4%) 2 (50.0%) 15 (57.7%)
Non-binary 1 (33.3%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 1 (3.8%)
Woman 1 (33.3%) 2 (28.6%) 3 (60.0%) 2 (28.6%) 2 (50.0%) 10 (38.5%)
Agent Learning Plots
NonDeviant Analysis
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: corrresp
                                   Chisq Df Pr(>Chisq)    
opinion_round                   195.4479  1  < 2.2e-16 ***
Deviant_threshold                33.2358  4  1.069e-06 ***
opinion_round:Deviant_threshold   7.0631  4     0.1326    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       opinion_round.trend      SE  df asymp.LCL asymp.UCL z.ratio p.value
 overall               0.113 0.00807 Inf    0.0976     0.129  14.052  <.0001

Results are averaged over the levels of: Deviant_threshold 
Confidence level used: 0.95 
$emmeans
 Deviant_threshold emmean    SE  df asymp.LCL asymp.UCL z.ratio p.value
 0                  1.533 0.100 Inf     1.336      1.73  15.293  <.0001
 0.25               1.003 0.109 Inf     0.789      1.22   9.218  <.0001
 0.5                0.850 0.103 Inf     0.648      1.05   8.273  <.0001
 0.75               0.863 0.109 Inf     0.649      1.08   7.905  <.0001
 1                  0.946 0.101 Inf     0.748      1.15   9.332  <.0001

Results are given on the logit (not the response) scale. 
Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df asymp.LCL
 Deviant_threshold0 - Deviant_threshold0.25      0.5301 0.147 Inf     0.129
 Deviant_threshold0 - Deviant_threshold0.5       0.6831 0.143 Inf     0.294
 Deviant_threshold0 - Deviant_threshold0.75      0.6698 0.147 Inf     0.268
 Deviant_threshold0 - Deviant_threshold1         0.5863 0.142 Inf     0.200
 Deviant_threshold0.25 - Deviant_threshold0.5    0.1530 0.149 Inf    -0.253
 Deviant_threshold0.25 - Deviant_threshold0.75   0.1397 0.153 Inf    -0.278
 Deviant_threshold0.25 - Deviant_threshold1      0.0562 0.148 Inf    -0.347
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.0133 0.149 Inf    -0.420
 Deviant_threshold0.5 - Deviant_threshold1      -0.0968 0.143 Inf    -0.488
 Deviant_threshold0.75 - Deviant_threshold1     -0.0835 0.148 Inf    -0.487
 asymp.UCL z.ratio p.value
     0.931   3.609  0.0028
     1.072   4.793  <.0001
     1.071   4.550  0.0001
     0.972   4.143  0.0003
     0.558   1.029  0.8420
     0.558   0.912  0.8925
     0.459   0.380  0.9956
     0.393  -0.089  1.0000
     0.294  -0.675  0.9619
     0.320  -0.564  0.9802

Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Similarity Plot
Similarity Analysis
Type III Analysis of Variance Table with Satterthwaite's method
                             Sum Sq Mean Sq NumDF DenDF  F value  Pr(>F)    
targetpair                      632     632     1   273   2.9882 0.08501 .  
Deviant_threshold             57300   57300     1   273 271.0453 < 2e-16 ***
targetpair:Deviant_threshold  42838   42838     1   273 202.6359 < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emtrends
 targetpair Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 DN                          -63.68 2.97 273    -69.5  -57.829 -21.415  <.0001
 NN                           -5.91 2.89 273    -11.6   -0.234  -2.050  0.0414

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 

$contrasts
 contrast estimate   SE  df lower.CL upper.CL t.ratio p.value
 DN - NN     -57.8 4.06 273    -65.8    -49.8 -14.235  <.0001

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 
ISM Plot
ISM Analysis
Analysis of Variance Table

Response: k
                   Df  Sum Sq Mean Sq F value    Pr(>F)    
Deviant_threshold   4  28.224  7.0559  14.391 1.174e-10 ***
Residuals         268 131.405  0.4903                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 Deviant_threshold emmean     SE  df lower.CL upper.CL t.ratio p.value
 0                   1.68 0.0889 268     1.50     1.85  18.869  <.0001
 0.25                1.65 0.0990 268     1.45     1.84  16.616  <.0001
 0.5                 2.11 0.0944 268     1.92     2.29  22.303  <.0001
 0.75                2.27 0.1000 268     2.07     2.46  22.660  <.0001
 1                   2.45 0.0927 268     2.27     2.63  26.424  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                                      estimate    SE  df lower.CL
 Deviant_threshold0 - Deviant_threshold0.25      0.0325 0.133 268   -0.333
 Deviant_threshold0 - Deviant_threshold0.5      -0.4278 0.130 268   -0.784
 Deviant_threshold0 - Deviant_threshold0.75     -0.5888 0.134 268   -0.956
 Deviant_threshold0 - Deviant_threshold1        -0.7728 0.128 268   -1.126
 Deviant_threshold0.25 - Deviant_threshold0.5   -0.4603 0.137 268   -0.836
 Deviant_threshold0.25 - Deviant_threshold0.75  -0.6213 0.141 268   -1.008
 Deviant_threshold0.25 - Deviant_threshold1     -0.8053 0.136 268   -1.178
 Deviant_threshold0.5 - Deviant_threshold0.75   -0.1610 0.138 268   -0.539
 Deviant_threshold0.5 - Deviant_threshold1      -0.3450 0.132 268   -0.708
 Deviant_threshold0.75 - Deviant_threshold1     -0.1840 0.136 268   -0.559
 upper.CL t.ratio p.value
   0.3981   0.244  0.9992
  -0.0716  -3.298  0.0097
  -0.2212  -4.399  0.0002
  -0.4199  -6.014  <.0001
  -0.0845  -3.364  0.0078
  -0.2347  -4.414  0.0001
  -0.4327  -5.935  <.0001
   0.2168  -1.170  0.7682
   0.0185  -2.606  0.0720
   0.1907  -1.349  0.6610

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
 Deviant_threshold emmean     SE  df null t.ratio p.value
 0                   1.68 0.0889 268    2  -3.621  0.0002
 0.25                1.65 0.0990 268    2  -3.580  0.0002
 0.5                 2.11 0.0944 268    2   1.120  0.8682
 0.75                2.27 0.1000 268    2   2.667  0.9959
 1                   2.45 0.0927 268    2   4.860  1.0000

P values are left-tailed 
New Agent Prediction Plot
Prediction Analysis
# A tibble: 2 × 13
  model    term              estimate std.error statistic p.value conf.low
  <chr>    <chr>                <dbl>     <dbl>     <dbl>   <dbl>    <dbl>
1 below_.5 Deviant_threshold    -16.3      10.0     -1.63   0.106    -36.1
2 above_.5 Deviant_threshold    -14.6      10.1     -1.44   0.151    -34.6
  conf.high r.squared adj.r.squared    df df.residual  nobs
      <dbl>     <dbl>         <dbl> <dbl>       <int> <int>
1      3.49    0.0158       0.00981     1         165   167
2      5.39    0.0129       0.00670     1         159   161
Analysis of Variance Table

Response: confidence
           Df Sum Sq Mean Sq F value  Pr(>F)  
deviance    4   7877 1969.31   2.734 0.02942 *
Residuals 268 193044  720.31                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 deviance emmean   SE  df lower.CL upper.CL t.ratio p.value
 0          61.1 3.41 268     54.4     67.8  17.915  <.0001
 0.25       53.2 3.80 268     45.8     60.7  14.027  <.0001
 0.5        53.1 3.62 268     45.9     60.2  14.660  <.0001
 0.75       48.7 3.83 268     41.2     56.3  12.711  <.0001
 1          45.8 3.55 268     38.8     52.8  12.871  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                    estimate   SE  df lower.CL upper.CL t.ratio
 deviance0 - deviance0.25       7.825 5.10 268    -6.19     21.8   1.534
 deviance0 - deviance0.5        8.010 4.97 268    -5.64     21.7   1.611
 deviance0 - deviance0.75      12.330 5.13 268    -1.76     26.4   2.403
 deviance0 - deviance1         15.310 4.92 268     1.78     28.8   3.109
 deviance0.25 - deviance0.5     0.185 5.24 268   -14.22     14.6   0.035
 deviance0.25 - deviance0.75    4.505 5.40 268   -10.31     19.3   0.835
 deviance0.25 - deviance1       7.486 5.20 268    -6.80     21.8   1.439
 deviance0.5 - deviance0.75     4.320 5.27 268   -10.16     18.8   0.819
 deviance0.5 - deviance1        7.300 5.07 268    -6.63     21.2   1.439
 deviance0.75 - deviance1       2.980 5.23 268   -11.38     17.3   0.570
 p.value
  0.5414
  0.4915
  0.1175
  0.0176
  1.0000
  0.9195
  0.6027
  0.9245
  0.6030
  0.9793

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 5 estimates 
P value adjustment: tukey method for comparing a family of 5 estimates 
Moderator: Last Opinion
0
(N=62)
0.25
(N=50)
0.5
(N=55)
0.75
(N=49)
1
(N=57)
Overall
(N=273)
pred_maj
Yes 50 (80.6%) 40 (80.0%) 41 (74.5%) 41 (83.7%) 41 (71.9%) 213 (78.0%)
No 12 (19.4%) 10 (20.0%) 14 (25.5%) 8 (16.3%) 16 (28.1%) 60 (22.0%)
# A tibble: 4 × 14
# Groups:   pred_maj [2]
  pred_maj id       term              estimate std.error statistic p.value
  <lgl>    <chr>    <chr>                <dbl>     <dbl>     <dbl>   <dbl>
1 FALSE    below_.5 Deviant_threshold    -3.97      21.4    -0.186   0.854
2 FALSE    above_.5 Deviant_threshold    -8.20      20.2    -0.406   0.687
3 TRUE     below_.5 Deviant_threshold   -18.7       11.3    -1.64    0.102
4 TRUE     above_.5 Deviant_threshold   -16.2       11.6    -1.40    0.165
  conf.low conf.high r.squared adj.r.squared    df df.residual  nobs
     <dbl>     <dbl>     <dbl>         <dbl> <dbl>       <int> <int>
1    -47.4     39.4    0.00101      -0.0284      1          34    36
2    -49.1     32.7    0.00457      -0.0231      1          36    38
3    -41.1      3.79   0.0205        0.0129      1         129   131
4    -39.3      6.80   0.0158        0.00770     1         121   123
Analysis of Variance Table

Response: confidence
                   Df Sum Sq Mean Sq F value  Pr(>F)  
deviance            4   7877  1969.3  2.7662 0.02795 *
pred_maj            1   3435  3435.3  4.8253 0.02892 *
deviance:pred_maj   4   2372   593.1  0.8330 0.50518  
Residuals         263 187236   711.9                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Order of deviant across rounds
Opinion Round
0
(N=273)
1
(N=273)
2
(N=273)
3
(N=273)
4
(N=273)
5
(N=273)
6
(N=273)
7
(N=273)
8
(N=273)
9
(N=273)
10
(N=273)
11
(N=273)
Overall
(N=3276)
trialnum
0 46 (16.8%) 49 (17.9%) 41 (15.0%) 44 (16.1%) 39 (14.3%) 48 (17.6%) 37 (13.6%) 48 (17.6%) 39 (14.3%) 47 (17.2%) 49 (17.9%) 63 (23.1%) 550 (16.8%)
1 49 (17.9%) 50 (18.3%) 43 (15.8%) 46 (16.8%) 42 (15.4%) 46 (16.8%) 48 (17.6%) 49 (17.9%) 46 (16.8%) 44 (16.1%) 52 (19.0%) 42 (15.4%) 557 (17.0%)
2 45 (16.5%) 41 (15.0%) 43 (15.8%) 39 (14.3%) 55 (20.1%) 44 (16.1%) 36 (13.2%) 54 (19.8%) 50 (18.3%) 53 (19.4%) 56 (20.5%) 39 (14.3%) 555 (16.9%)
3 43 (15.8%) 43 (15.8%) 43 (15.8%) 46 (16.8%) 43 (15.8%) 44 (16.1%) 58 (21.2%) 41 (15.0%) 36 (13.2%) 41 (15.0%) 39 (14.3%) 41 (15.0%) 518 (15.8%)
4 41 (15.0%) 41 (15.0%) 47 (17.2%) 50 (18.3%) 57 (20.9%) 51 (18.7%) 45 (16.5%) 42 (15.4%) 57 (20.9%) 44 (16.1%) 35 (12.8%) 45 (16.5%) 555 (16.9%)
5 49 (17.9%) 49 (17.9%) 56 (20.5%) 48 (17.6%) 37 (13.6%) 40 (14.7%) 49 (17.9%) 39 (14.3%) 45 (16.5%) 44 (16.1%) 42 (15.4%) 43 (15.8%) 541 (16.5%)
Unresolved
  • all good